Choosing K (elbow method, silhouette score) in ML Python - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the KMeans class from scikit-learn.

ML Python

from sklearn.cluster import [1]

Drag options to blanks, or click blank then click option'

ADecisionTreeClassifier

BLinearRegression

CPCA

DKMeans

Attempts:

3 left

💡 Hint

Common Mistakes

Importing a regression or classification model instead of KMeans.

Misspelling the class name.

The KMeans class is used for clustering in scikit-learn. Importing it correctly allows us to create KMeans models.

2fill in blank

medium

Complete the code to fit a KMeans model with 3 clusters on data X.

ML Python

model = KMeans(n_clusters=[1])
model.fit(X)

Drag options to blanks, or click blank then click option'

A3

B1

C10

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using too many or too few clusters by mistake.

Confusing cluster count with other parameters.

Setting n_clusters=3 tells the model to find 3 groups in the data.

3fill in blank

hard

Fix the error in the code to compute the silhouette score for clustering labels.

ML Python

from sklearn.metrics import silhouette_score
score = silhouette_score(X, [1])

Drag options to blanks, or click blank then click option'

Amodel.fit(X)

Bmodel.predict(X)

Cmodel.labels_

DX

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the data X instead of labels.

Calling fit inside silhouette_score argument.

The silhouette_score function needs the cluster labels, which are stored in model.labels_ after fitting.

4fill in blank

hard

Fill both blanks to create a list of inertia values for K from 1 to 5.

ML Python

inertia_values = []
for k in range(1, 6):
    model = KMeans(n_clusters=[1])
    model.fit(X)
    inertia_values.append([2])

Drag options to blanks, or click blank then click option'

Ak

Bmodel.inertia_

Cmodel.score(X)

DX

Attempts:

3 left

💡 Hint

Common Mistakes

Appending model.score(X) which returns negative inertia.

Using a fixed number instead of k for clusters.

We loop over k values and set n_clusters=k. The inertia (sum of squared distances) is accessed by model.inertia_.

5fill in blank

hard

Fill all three blanks to compute silhouette scores for K from 2 to 6 and store them in a dictionary.

ML Python

silhouette_scores = {}
for k in range(2, 7):
    model = KMeans(n_clusters=[1])
    labels = model.fit_predict(X)
    silhouette_scores[[2]] = [3](X, labels)

Drag options to blanks, or click blank then click option'

Ak

Csilhouette_score

Dmodel.inertia_

Attempts:

3 left

💡 Hint

Common Mistakes

Using inertia instead of silhouette_score.

Using wrong keys in the dictionary.

We use k for the number of clusters and as the dictionary key. The silhouette score is computed by calling silhouette_score(X, labels).

Practice

1. What is the main goal when choosing the number of clusters K in clustering algorithms?

easy

A. To find the number of groups that best represent the data

B. To maximize the number of clusters regardless of data

C. To minimize the number of clusters to one

D. To randomly select a number without analysis

Solution

1. Step 1: Understand the purpose of clustering

   Clustering groups similar data points together to find patterns.

2. Step 2: Identify the role of choosing K

   Choosing K means deciding how many groups best represent the data structure.

3. Final Answer:

   To find the number of groups that best represent the data -> Option A

4. Quick Check:

   Choosing K = best data groups [OK]

Hint: Choose K to best represent data groups, not randomly [OK]

Common Mistakes:

• Picking K without checking data patterns
• Choosing too many clusters blindly
• Ignoring the meaning of clusters

2. Which of the following Python code snippets correctly computes the silhouette score for clustering results stored in labels with data X?

easy

A. from sklearn.metrics import silhouette_score
score = silhouette_score(labels, X)

B. from sklearn.cluster import silhouette_score
score = silhouette_score(labels, X)

C. from sklearn.metrics import silhouette_score
score = silhouette_score(X, labels)

D. from sklearn.cluster import silhouette_score
score = silhouette_score(X, labels)

Solution

1. Step 1: Check the correct import

   The silhouette_score function is in sklearn.metrics, not sklearn.cluster.

2. Step 2: Verify function parameters order

   The function takes data first (X), then cluster labels (labels).

3. Final Answer:

   from sklearn.metrics import silhouette_score\nscore = silhouette_score(X, labels) -> Option C

4. Quick Check:

   Correct import and parameter order = from sklearn.metrics import silhouette_score score = silhouette_score(X, labels) [OK]

Hint: Import from metrics and pass data first, labels second [OK]

Common Mistakes:

• Importing silhouette_score from wrong module
• Swapping data and labels in function call
• Using cluster module instead of metrics

3. Given the following code, what will be the printed silhouette score?

from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
import numpy as np

X = np.array([[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]])
kmeans = KMeans(n_clusters=2, random_state=42).fit(X)
labels = kmeans.labels_
score = silhouette_score(X, labels)
print(round(score, 2))

medium

A. 0.50

B. 0.74

C. 0.30

D. 1.00

Solution

1. Step 1: Understand the data and clustering

   The data has two clear groups around [1, x] and [10, x], so KMeans with 2 clusters fits well.

2. Step 2: Calculate silhouette score

   Silhouette score measures cluster quality; for well-separated clusters, it is close to 1. Running the code gives approximately 0.74.

3. Final Answer:

   0.74 -> Option B

4. Quick Check:

   Well-separated clusters give silhouette ~0.74 [OK]

Hint: Well-separated clusters usually have silhouette > 0.7 [OK]

Common Mistakes:

• Expecting silhouette score to be 1.0 always
• Confusing silhouette with inertia
• Ignoring cluster separation in score

4. You run the elbow method but the inertia keeps decreasing smoothly without a clear elbow point. What is the best way to fix this issue?

medium

A. Try silhouette score to find the best K instead

B. Increase the number of clusters to the maximum possible

C. Ignore the elbow method and pick K=1

D. Use random K values without checking metrics

Solution

1. Step 1: Identify the problem with elbow method

   If inertia decreases smoothly, no clear elbow means it's hard to pick K by this method.

2. Step 2: Use alternative metric

   Silhouette score measures cluster quality differently and can help find the best K when elbow is unclear.

3. Final Answer:

   Try silhouette score to find the best K instead -> Option A

4. Quick Check:

   Use silhouette when elbow is unclear [OK]

Hint: Switch to silhouette score if elbow is unclear [OK]

Common Mistakes:

• Forcing a large K without reason
• Ignoring metrics and guessing K
• Picking K=1 without analysis

5. You have a dataset with 5 natural clusters but the elbow method suggests K=3 and silhouette score suggests K=5. Which K should you choose and why?

hard

A. Choose K=3 because elbow method always gives the best K

B. Choose K=10 to overfit the data

C. Choose K=1 to simplify the model

D. Choose K=5 because silhouette score better reflects cluster separation

Solution

1. Step 1: Compare elbow and silhouette methods

   Elbow method focuses on inertia reduction, which can miss subtle clusters; silhouette measures cluster quality and separation.

2. Step 2: Match method to data nature

   Since the dataset has 5 natural clusters, silhouette score's suggestion aligns better with true structure.

3. Final Answer:

   Choose K=5 because silhouette score better reflects cluster separation -> Option D

4. Quick Check:

   Silhouette score > elbow for true cluster count [OK]

Hint: Trust silhouette score for natural cluster counts [OK]

Common Mistakes:

• Blindly trusting elbow method over silhouette
• Choosing too few clusters ignoring data
• Overfitting by choosing too many clusters